Mathematical World 2005; 392 pp; softcover ISBN-10: 0-8218-3859-8 ISBN-13: 978-0-8218-3859-4 List Price: US$83 Member Price: US$66.40 Order Code: MAWRLD-GSET
![[Add Item]](/images/addtocart.gif) | This three-volume set addresses the interplay between topology, functions, geometry, and algebra. Bringing the beauty and fun of mathematics to the classroom, the authors offer serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. It is suitable for advanced high-school students, graduate students, and researchers. The three-volume set includes A Mathematical Gift I, II, and III.  Readership
Advanced high-school students and undergraduates in mathematics. Table of Contents Part I
Invitation to topology (Viewing figures globally) - Introduction
- The Euler characteristic
- Vortices created by winds and the Euler characteristic
- Curvature of a surface and the Euler characteristic
The story of dimension - Introduction
- Learning to appreciate dimension
- What is dimension?
- Three-dimensional figures
- Physics and dimension
Part II
The legacy of trigonometric functions - Introduction
- Trigonometric functions and infinite series
- Elliptic functions
Intersection of geometry and algebra - Introduction
- The Poncelet closure theorem
- The Poncelet theorem for circles
- The Poncelet theorem in the world of complex numbers
- Proof of the Poncelet theorem using plane geometry
- Conclusion
Part III
- The story of the birth of manifolds
- The prelude to the birth of manifolds
- The birth of manifolds
- The story of area and volume from everyday notions to mathematical concepts
- Transition from the notion of "size" to the concept of "area"
- Scissors-congruent polygons
- Scissors-congruent polyhedra
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